High and low estrogen in terms of diet really has more to do with dietary fat than any particular food. Here is a study on estrogen levels and diet (omnivore versus vegetarian):
It makes sense that a diet heavy in dairy, eggs, and meat would be higher in fat and lower in fiber. Fat is also a necessary component in the utilization of steriod sex hormones (as well as vitamin D and other hormones). Absorption and storage of estrogen is higher with a higher body fat, but also with a regular menstrual cycle. Maintaining a normal healthy weight is also important in terms of estrogen in females.
As a vegan, you could still get enough dietary fat by concentrating on plant sources such as nuts, seeds, peanuts/butter, avocado, olives, coconut, soy products. Increase those and decrease fruits, vegetables, and grains slightly if estrogen, weight, and dietary fat is an issue. From your past posts, I know that low weight is an issue for you, and that will certainly contribute to low estrogen.
I am postmenopausal (due to loss of ovaries 11 years ago) so do not menstruate. However, I do take a straight estradiol replacement patch in order to stave off symptoms of menopause (which for my young age and surgical menopause status are much more intense than for someone in natural menopause) and to help protect my bone density or at least keep it from getting rapidly worse.
Many years ago when I was a teen, I did not get my first period until I was 16. I was an omni then, but was ballet/modern dance training 22 hours per week and was slightly underweight with all that activity. At 16 puberty finally hit and I gained a good bit of weight and with it my period. It had everything to do with body fat and little to do with what I ate in particular.